Riis struck in the 89th minute at Deepdale, running on to Alan Browne’s pass to drive a low finish across the Cherries keeper into the far corner.
The Dane had come on as a substitute for Ched Evans, that his third game in a row on the bench.
He’s now on 17 goals for the season in league and cup, five of those scored in the 89th minute or later.
North End had fallen behind five minutes into the second half to a Jamal Lowe goal before Cameron Archer quickly equalised.
The stage was then set for Riis to score the winner and deliver a first home victory since December 11.
PNE manager Lowe said: “I’d call that a ‘shoving one up the gaffer’ moment from Emil.
"Every player wants to start and Emil might have been disappointed last Friday when he found out he wasn’t starting.
"I had been toying with starting him and Cameron but I felt to get us up the pitch we needed Ched’s strength to begin with and then Emil later on.
"Players don’t want to hear that, thinking they might get 15/20 minutes at the end because they want to start every game.
"I know what Emil can do, he can be a world beater if he wants to be. He’s scored 17 goals now and I’m expecting him to go beyond 20.
"It was a good pass from Browney for his goal and Daniel Johnson set up Cameron’s goal.
"Browney and DJ are two key players and if they perform, the team performs. It was two assists from two good midfielders to get us two goals from two good strikers.”
Lowe was delighted to savour a home victory, his only other one as PNE boss coming in his first game in charge.
"You want to win as many home games as you possibly can but I won’t complain too much because we’ve won more on the road than we were expected to,” said Lowe.
"This was an important win against a very good side who I expect will go up.”